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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 02 Nov 2009 15:32:55 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/02/t1257201274514150ppochdw1p.htm/, Retrieved Fri, 03 May 2024 16:01:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=53057, Retrieved Fri, 03 May 2024 16:01:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Workshop 2: Afzet...] [2009-11-01 22:03:19] [b458cdfea59edb592ddaf846f3f56c20]
- RMPD    [Central Tendency] [Mediaan afzetprij...] [2009-11-02 22:32:55] [95223d06eb2c638c714cd6fbd03e9e6c] [Current]
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Dataseries X:
121
119.9
120.2
119.6
118.9
119.2
121.8
123.9
125.1
128.8
131.7
133.1
132.9
134
132.7
130.8
129.5
128.9
127.4
125.6
123.5
122.4
119.9
118.8
117.9
117.7
117.4
117.3
117.1
117.2
117
116.8
116.7
116.8
116.3
116.3
115.8
115.8
115.6
114.8
114.5
113.7
112.8
112.4
110.8
110
109.9
109.5
109.5
109.4
109.4
109.4
109.7
109.9
110.1
110.6
109.2
109.5
109.8
108.8
108.7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=53057&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=53057&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=53057&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean117.9295081967210.946530461211689124.591350230562
Geometric Mean117.706750842057
Harmonic Mean117.489212854993
Quadratic Mean118.157200789290
Winsorized Mean ( 1 / 20 )117.9163934426230.94219595936055125.150604044885
Winsorized Mean ( 2 / 20 )117.9229508196720.938369686789472125.667903044836
Winsorized Mean ( 3 / 20 )117.9229508196720.934255185189028126.221350107693
Winsorized Mean ( 4 / 20 )117.8573770491800.917362753143275128.474125034345
Winsorized Mean ( 5 / 20 )117.7836065573770.89918354079854130.989504604118
Winsorized Mean ( 6 / 20 )117.6655737704920.867673496440736135.610427485875
Winsorized Mean ( 7 / 20 )117.5967213114750.852235784138201137.986134236773
Winsorized Mean ( 8 / 20 )117.5836065573770.849342980814814138.440664388106
Winsorized Mean ( 9 / 20 )117.4065573770490.800375147192206146.689409071387
Winsorized Mean ( 10 / 20 )117.1278688524590.738700421200397158.559363838083
Winsorized Mean ( 11 / 20 )117.0557377049180.718683239580105162.875285325018
Winsorized Mean ( 12 / 20 )116.8196721311480.676017022420153172.805814434866
Winsorized Mean ( 13 / 20 )116.7557377049180.657647424059793177.535459629965
Winsorized Mean ( 14 / 20 )116.5262295081970.61185421689211190.447701905345
Winsorized Mean ( 15 / 20 )116.5016393442620.567125297222895205.424868040182
Winsorized Mean ( 16 / 20 )116.3442622950820.526128890845501221.132624190461
Winsorized Mean ( 17 / 20 )116.5672131147540.416941251457004279.577069209174
Winsorized Mean ( 18 / 20 )116.5967213114750.384629317066543303.140494335494
Winsorized Mean ( 19 / 20 )116.8770491803280.339642961382271344.117389345165
Winsorized Mean ( 20 / 20 )117.0409836065570.284973175318763410.708774521106
Trimmed Mean ( 1 / 20 )117.8135593220340.926086193503231127.216624271618
Trimmed Mean ( 2 / 20 )117.7035087719300.905846247584219129.937623615300
Trimmed Mean ( 3 / 20 )117.5818181818180.882901899249051133.176537825807
Trimmed Mean ( 4 / 20 )117.4509433962260.855858418841803137.231743954996
Trimmed Mean ( 5 / 20 )117.3294117647060.828451397831992141.624978932681
Trimmed Mean ( 6 / 20 )117.2163265306120.799975270338311146.524937553434
Trimmed Mean ( 7 / 20 )117.1191489361700.77373416242071151.368718901787
Trimmed Mean ( 8 / 20 )117.0266666666670.744368758401942157.215983806073
Trimmed Mean ( 9 / 20 )116.9279069767440.70648260402001165.507128287949
Trimmed Mean ( 10 / 20 )116.8487804878050.671384826139949174.041437843649
Trimmed Mean ( 11 / 20 )116.8051282051280.643087910764126181.631665360244
Trimmed Mean ( 12 / 20 )116.7675675675680.610445291787132191.282608185445
Trimmed Mean ( 13 / 20 )116.760.578555140345472201.813088948236
Trimmed Mean ( 14 / 20 )116.7606060606060.539358825891479216.480384589273
Trimmed Mean ( 15 / 20 )116.7935483870970.498383094948613234.34492375617
Trimmed Mean ( 16 / 20 )116.8344827586210.454216042595869257.222272667661
Trimmed Mean ( 17 / 20 )116.9037037037040.402325203377786290.570172393427
Trimmed Mean ( 18 / 20 )116.9520.370635490295610315.544525719116
Trimmed Mean ( 19 / 20 )117.0043478260870.333947420825895350.367574442468
Trimmed Mean ( 20 / 20 )117.0238095238100.297281713587567393.646175244274
Median117
Midrange121.35
Midmean - Weighted Average at Xnp116.626666666667
Midmean - Weighted Average at X(n+1)p116.793548387097
Midmean - Empirical Distribution Function116.793548387097
Midmean - Empirical Distribution Function - Averaging116.793548387097
Midmean - Empirical Distribution Function - Interpolation116.793548387097
Midmean - Closest Observation116.584375
Midmean - True Basic - Statistics Graphics Toolkit116.793548387097
Midmean - MS Excel (old versions)116.793548387097
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 117.929508196721 & 0.946530461211689 & 124.591350230562 \tabularnewline
Geometric Mean & 117.706750842057 &  &  \tabularnewline
Harmonic Mean & 117.489212854993 &  &  \tabularnewline
Quadratic Mean & 118.157200789290 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 117.916393442623 & 0.94219595936055 & 125.150604044885 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 117.922950819672 & 0.938369686789472 & 125.667903044836 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 117.922950819672 & 0.934255185189028 & 126.221350107693 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 117.857377049180 & 0.917362753143275 & 128.474125034345 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 117.783606557377 & 0.89918354079854 & 130.989504604118 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 117.665573770492 & 0.867673496440736 & 135.610427485875 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 117.596721311475 & 0.852235784138201 & 137.986134236773 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 117.583606557377 & 0.849342980814814 & 138.440664388106 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 117.406557377049 & 0.800375147192206 & 146.689409071387 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 117.127868852459 & 0.738700421200397 & 158.559363838083 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 117.055737704918 & 0.718683239580105 & 162.875285325018 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 116.819672131148 & 0.676017022420153 & 172.805814434866 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 116.755737704918 & 0.657647424059793 & 177.535459629965 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 116.526229508197 & 0.61185421689211 & 190.447701905345 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 116.501639344262 & 0.567125297222895 & 205.424868040182 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 116.344262295082 & 0.526128890845501 & 221.132624190461 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 116.567213114754 & 0.416941251457004 & 279.577069209174 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 116.596721311475 & 0.384629317066543 & 303.140494335494 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 116.877049180328 & 0.339642961382271 & 344.117389345165 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 117.040983606557 & 0.284973175318763 & 410.708774521106 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 117.813559322034 & 0.926086193503231 & 127.216624271618 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 117.703508771930 & 0.905846247584219 & 129.937623615300 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 117.581818181818 & 0.882901899249051 & 133.176537825807 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 117.450943396226 & 0.855858418841803 & 137.231743954996 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 117.329411764706 & 0.828451397831992 & 141.624978932681 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 117.216326530612 & 0.799975270338311 & 146.524937553434 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 117.119148936170 & 0.77373416242071 & 151.368718901787 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 117.026666666667 & 0.744368758401942 & 157.215983806073 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 116.927906976744 & 0.70648260402001 & 165.507128287949 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 116.848780487805 & 0.671384826139949 & 174.041437843649 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 116.805128205128 & 0.643087910764126 & 181.631665360244 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 116.767567567568 & 0.610445291787132 & 191.282608185445 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 116.76 & 0.578555140345472 & 201.813088948236 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 116.760606060606 & 0.539358825891479 & 216.480384589273 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 116.793548387097 & 0.498383094948613 & 234.34492375617 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 116.834482758621 & 0.454216042595869 & 257.222272667661 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 116.903703703704 & 0.402325203377786 & 290.570172393427 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 116.952 & 0.370635490295610 & 315.544525719116 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 117.004347826087 & 0.333947420825895 & 350.367574442468 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 117.023809523810 & 0.297281713587567 & 393.646175244274 \tabularnewline
Median & 117 &  &  \tabularnewline
Midrange & 121.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 116.626666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 116.793548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 116.793548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 116.793548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 116.793548387097 &  &  \tabularnewline
Midmean - Closest Observation & 116.584375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 116.793548387097 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 116.793548387097 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=53057&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]117.929508196721[/C][C]0.946530461211689[/C][C]124.591350230562[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]117.706750842057[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]117.489212854993[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]118.157200789290[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]117.916393442623[/C][C]0.94219595936055[/C][C]125.150604044885[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]117.922950819672[/C][C]0.938369686789472[/C][C]125.667903044836[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]117.922950819672[/C][C]0.934255185189028[/C][C]126.221350107693[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]117.857377049180[/C][C]0.917362753143275[/C][C]128.474125034345[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]117.783606557377[/C][C]0.89918354079854[/C][C]130.989504604118[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]117.665573770492[/C][C]0.867673496440736[/C][C]135.610427485875[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]117.596721311475[/C][C]0.852235784138201[/C][C]137.986134236773[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]117.583606557377[/C][C]0.849342980814814[/C][C]138.440664388106[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]117.406557377049[/C][C]0.800375147192206[/C][C]146.689409071387[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]117.127868852459[/C][C]0.738700421200397[/C][C]158.559363838083[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]117.055737704918[/C][C]0.718683239580105[/C][C]162.875285325018[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]116.819672131148[/C][C]0.676017022420153[/C][C]172.805814434866[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]116.755737704918[/C][C]0.657647424059793[/C][C]177.535459629965[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]116.526229508197[/C][C]0.61185421689211[/C][C]190.447701905345[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]116.501639344262[/C][C]0.567125297222895[/C][C]205.424868040182[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]116.344262295082[/C][C]0.526128890845501[/C][C]221.132624190461[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]116.567213114754[/C][C]0.416941251457004[/C][C]279.577069209174[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]116.596721311475[/C][C]0.384629317066543[/C][C]303.140494335494[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]116.877049180328[/C][C]0.339642961382271[/C][C]344.117389345165[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]117.040983606557[/C][C]0.284973175318763[/C][C]410.708774521106[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]117.813559322034[/C][C]0.926086193503231[/C][C]127.216624271618[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]117.703508771930[/C][C]0.905846247584219[/C][C]129.937623615300[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]117.581818181818[/C][C]0.882901899249051[/C][C]133.176537825807[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]117.450943396226[/C][C]0.855858418841803[/C][C]137.231743954996[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]117.329411764706[/C][C]0.828451397831992[/C][C]141.624978932681[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]117.216326530612[/C][C]0.799975270338311[/C][C]146.524937553434[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]117.119148936170[/C][C]0.77373416242071[/C][C]151.368718901787[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]117.026666666667[/C][C]0.744368758401942[/C][C]157.215983806073[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]116.927906976744[/C][C]0.70648260402001[/C][C]165.507128287949[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]116.848780487805[/C][C]0.671384826139949[/C][C]174.041437843649[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]116.805128205128[/C][C]0.643087910764126[/C][C]181.631665360244[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]116.767567567568[/C][C]0.610445291787132[/C][C]191.282608185445[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]116.76[/C][C]0.578555140345472[/C][C]201.813088948236[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]116.760606060606[/C][C]0.539358825891479[/C][C]216.480384589273[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]116.793548387097[/C][C]0.498383094948613[/C][C]234.34492375617[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]116.834482758621[/C][C]0.454216042595869[/C][C]257.222272667661[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]116.903703703704[/C][C]0.402325203377786[/C][C]290.570172393427[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]116.952[/C][C]0.370635490295610[/C][C]315.544525719116[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]117.004347826087[/C][C]0.333947420825895[/C][C]350.367574442468[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]117.023809523810[/C][C]0.297281713587567[/C][C]393.646175244274[/C][/ROW]
[ROW][C]Median[/C][C]117[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]121.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]116.626666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]116.793548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]116.793548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]116.793548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]116.793548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]116.584375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]116.793548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]116.793548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=53057&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=53057&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean117.9295081967210.946530461211689124.591350230562
Geometric Mean117.706750842057
Harmonic Mean117.489212854993
Quadratic Mean118.157200789290
Winsorized Mean ( 1 / 20 )117.9163934426230.94219595936055125.150604044885
Winsorized Mean ( 2 / 20 )117.9229508196720.938369686789472125.667903044836
Winsorized Mean ( 3 / 20 )117.9229508196720.934255185189028126.221350107693
Winsorized Mean ( 4 / 20 )117.8573770491800.917362753143275128.474125034345
Winsorized Mean ( 5 / 20 )117.7836065573770.89918354079854130.989504604118
Winsorized Mean ( 6 / 20 )117.6655737704920.867673496440736135.610427485875
Winsorized Mean ( 7 / 20 )117.5967213114750.852235784138201137.986134236773
Winsorized Mean ( 8 / 20 )117.5836065573770.849342980814814138.440664388106
Winsorized Mean ( 9 / 20 )117.4065573770490.800375147192206146.689409071387
Winsorized Mean ( 10 / 20 )117.1278688524590.738700421200397158.559363838083
Winsorized Mean ( 11 / 20 )117.0557377049180.718683239580105162.875285325018
Winsorized Mean ( 12 / 20 )116.8196721311480.676017022420153172.805814434866
Winsorized Mean ( 13 / 20 )116.7557377049180.657647424059793177.535459629965
Winsorized Mean ( 14 / 20 )116.5262295081970.61185421689211190.447701905345
Winsorized Mean ( 15 / 20 )116.5016393442620.567125297222895205.424868040182
Winsorized Mean ( 16 / 20 )116.3442622950820.526128890845501221.132624190461
Winsorized Mean ( 17 / 20 )116.5672131147540.416941251457004279.577069209174
Winsorized Mean ( 18 / 20 )116.5967213114750.384629317066543303.140494335494
Winsorized Mean ( 19 / 20 )116.8770491803280.339642961382271344.117389345165
Winsorized Mean ( 20 / 20 )117.0409836065570.284973175318763410.708774521106
Trimmed Mean ( 1 / 20 )117.8135593220340.926086193503231127.216624271618
Trimmed Mean ( 2 / 20 )117.7035087719300.905846247584219129.937623615300
Trimmed Mean ( 3 / 20 )117.5818181818180.882901899249051133.176537825807
Trimmed Mean ( 4 / 20 )117.4509433962260.855858418841803137.231743954996
Trimmed Mean ( 5 / 20 )117.3294117647060.828451397831992141.624978932681
Trimmed Mean ( 6 / 20 )117.2163265306120.799975270338311146.524937553434
Trimmed Mean ( 7 / 20 )117.1191489361700.77373416242071151.368718901787
Trimmed Mean ( 8 / 20 )117.0266666666670.744368758401942157.215983806073
Trimmed Mean ( 9 / 20 )116.9279069767440.70648260402001165.507128287949
Trimmed Mean ( 10 / 20 )116.8487804878050.671384826139949174.041437843649
Trimmed Mean ( 11 / 20 )116.8051282051280.643087910764126181.631665360244
Trimmed Mean ( 12 / 20 )116.7675675675680.610445291787132191.282608185445
Trimmed Mean ( 13 / 20 )116.760.578555140345472201.813088948236
Trimmed Mean ( 14 / 20 )116.7606060606060.539358825891479216.480384589273
Trimmed Mean ( 15 / 20 )116.7935483870970.498383094948613234.34492375617
Trimmed Mean ( 16 / 20 )116.8344827586210.454216042595869257.222272667661
Trimmed Mean ( 17 / 20 )116.9037037037040.402325203377786290.570172393427
Trimmed Mean ( 18 / 20 )116.9520.370635490295610315.544525719116
Trimmed Mean ( 19 / 20 )117.0043478260870.333947420825895350.367574442468
Trimmed Mean ( 20 / 20 )117.0238095238100.297281713587567393.646175244274
Median117
Midrange121.35
Midmean - Weighted Average at Xnp116.626666666667
Midmean - Weighted Average at X(n+1)p116.793548387097
Midmean - Empirical Distribution Function116.793548387097
Midmean - Empirical Distribution Function - Averaging116.793548387097
Midmean - Empirical Distribution Function - Interpolation116.793548387097
Midmean - Closest Observation116.584375
Midmean - True Basic - Statistics Graphics Toolkit116.793548387097
Midmean - MS Excel (old versions)116.793548387097
Number of observations61



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')